Timeline for How to prove Liouville measure is invariant under geodesic flow?
Current License: CC BY-SA 3.0
2 events
| when toggle format | what | by | license | comment | |
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| Jan 24, 2023 at 17:37 | comment | added | Mizar | It seems that one needs the identity $\frac{d}{dt}\langle d\Phi_t(p)[e_i],e_j\rangle|_{t=0}=\langle\nabla_{e_i}X,e_j\rangle$ for a fixed $p\in SM$ and an orthonormal frame $\{e_i\}$ (of $TSM$) parallel at $p$ (the first scalar product is computed at $\Phi_t(p)$ and the second one at $p$). However, this seems to require that $\nabla$ is torsion-free. | |
| Dec 9, 2015 at 9:18 | history | answered | Matthias Ludewig | CC BY-SA 3.0 |